Interstate highway 45 is submerged from the effects of Hurricane Harvey - REUTERS

Tropical Storm Harvey sent devastating floods pouring into the nation's fourth-largest city on Sunday as rising water chased thousands of people to rooftops or higher ground and overwhelmed rescuers who could not keep up with the constant calls for help.

The incessant rain covered much of Houston in turbid, gray-green water and turned streets into rivers navigable only by boat. In a rescue effort that recalled the aftermath of Hurricane Katrina, helicopters landed near flooded freeways, airboats buzzed across submerged neighborhoods and high-water vehicles plowed through water-logged intersections. Some people managed with kayaks or canoes or swam.

Hurricane Harvey hits Texas, in pictures

Volunteers joined emergency teams to pull people from their homes or from the water, which was high enough in places to gush into second floors. The flooding was so widespread that authorities had trouble pinpointing the worst areas. They urged people to get on top of their houses to avoid becoming trapped in attics and to wave sheets or towels to draw attention to their location.

Debris lies on the ground after a building was destroyed by Hurricane Harvey in Aransas PassCredit: Gabe Hernandez

Judging from federal disaster declarations, the storm has so far affected about a quarter of the Texas population, or 6.8 million people in 18 counties. It was blamed for at least two deaths.

As the water rose, the National Weather Service issued another ominous forecast: Before the storm that arrived on Friday as a Category 4 hurricane is gone, some parts of Houston and its suburbs could get as much as 50 inches (1.3 meters) of rain. That would be the highest amount ever recorded in Texas.

Residents at La Vita Bella nursing home in Dickinson Texas sit in flood waters as they wait to be rescuedCredit: @DivendsMGR

Some areas have already received about half that amount. Since Thursday, South Houston recorded nearly 25 inches (63 centimeters), and the suburbs of Santa Fe and Dayton got 27 inches (69 centimeters).

"The breadth and intensity of this rainfall is beyond anything experienced before," the National Weather Service said in a statement.

Meteorologists said it was threatening to be America’s worst flood disaster in history with as much as 50 inches of rain forecast to fall on a heavily populated area.

Houston, America’s fourth biggest city, was one of the worst affected areas with 25 inches of rain falling by Sunday morning. The mayor said authorities had received 2000 calls for help and that the city’s convention centre was opening for people flooded out of their homes.

A car is submerged on a freeway flooded by Tropical Storm Harvey Credit: AP

"I don't need to tell anyone this is a very, very serious and unprecedented storm," said Sylvester Turner. "We have several hundred structural flooding reports. We expect that number to rise pretty dramatically."

Steve Bowen, chief meteorologist at reinsurance firm Aon Benfield, said it was "the most devastating flood event in Houston’s recorded history".

President Donald Trump plans to go to Texas on Tuesday to survey damage from the storm, a White House spokeswoman said on Sunday.

The theatre district of Houston is floodedCredit: AFP

"HISTORIC rainfall in Houston, and all over Texas. Floods are unprecedented, and more rain coming. Spirit of the people is incredible. Thanks!" he tweeted on Sunday evening.

By Sunday afternoon, water had risen high enough to reach the second floor of many buildings. People could be seen using inflatable beach toys, rubber rafts and air mattresses to make their way through streets that had turned into rivers.

“There’s flooding all over this city,” said Art Acevedo, Houston Police Chief, as he appealed for people to stay at home. “We have one fatality, and a potential second fatality from the flood waters out here.”

The strongest hurricane to hit the US in more than a decade barrelled ashore late on Friday night. It arrived as a category four storm – the second highest classification.

It uprooted trees, destroyed roofs and flipped parked cars as it moved inland.

In Rockport, where it came ashore, recreational vehicles were swatted over in a forecourt where they were on display.

“It was terrible,” Joel Valdez, 57, told Reuters. The storm ripped part of the roof from his trailer home at about 4 am, he said as he huddled in his Jeep for safety. "I could feel the whole house move."

Harvey’s winds had eased by Sunday morning. The storm’s energy ebbed as it meandered inland away from the warm waters of the Gulf of Mexico. But as its first assault ended, its second began.

Hurricane Harvey path

With the storm almost stationary it dumped torrential rain over a wide area that included Houston, with a population of more than six million people across its greater metropolitan area. It is known as a flood-prone place even at the best of times.

Its network of bayou streams was rapidly overwhelmed as rain fell at the rate of three inches per hour, leaving streets and underpasses under water.

The escalating sense of crisis was visible on social media, as hundreds of people messaged officials in search of help.

A woman stands on her front door as she surveys her property devastated by Hurricane Harvey in Rockport, TexasCredit: REUTERS/Adrees Latif

Ed Gonzales, Harris County Sheriff, made multiple requests for people to “shelter in place” if they could and admitted that emergency services had been overwhelmed by 911 calls.

He provided a non-stop rescue service, directing an ambulance to a woman going into a labour, someone suffering a heart attack, and responding to reports of a woman and child trapped in a submerged car, and another woman who posted: “I have 2 children with me and water is swallowing us up.”

A boat sits on a dock after Hurricane Harvey passed through Port Aransas, TexasCredit: Nick Wagner

“Getting lots of requests for hi-water rescues,” he wrote at one point. “Some involve children, others with medical issues. Trying to get to as many as possible.”

Meanwhile, the National Weather Service said 12 tornadoes had been reported across the region.

He has been monitoring developments from Camp David where he signed a disaster proclamation, freeing federal aid to help emergency efforts. On Sunday morning, he held a cabinet meeting by teleconference and said Texas was experiencing the sort of storm seen only once in 500 years.

“Many people are now saying that this is the worst storm/hurricane they have ever seen. Good news is that we have great talent on the ground,” he wrote on Twitter. “I will be going to Texas as soon as that trip can be made without causing disruption. The focus must be life and safety.”

Even as the authorities cope with the unfolding disaster, longer term recovery efforts have begun.

Brock Long, the head of the Federal Emergency Management Agency (Fema), said it would take years for the area to rebuild.

“Fema’s going to be there for years,” he said. “This disaster is going to be a landmark event and we’re already - while we are focussed on response right now in helping Texas respond - we are already pushing forward recovery housing teams.”